Final answer:
To find the length of the base of a parallelogram given the height, one must also know the area of the parallelogram to use the formula base = Area / height. To calculate the area of a triangle with a given base of 166 mm and a height of 930.0 mm, convert the dimensions to meters and use the area formula 1/2 x base x height, rounding to three significant figures for the answer.
Step-by-step explanation:
To calculate the length of the base of a parallelogram when given the height, you first need to know the area of the parallelogram. The area of a parallelogram is calculated by the formula: Area = base × height. If you only know the height, then you would need the area to find the base length by rearranging the formula to base = Area / height.
However, if you are asking about finding the area of a triangle with a given base and height, such as in the scenario where the triangle's base is 166 mm and its height is 930.0 mm, you'll use the formula for the area of a triangle, which is Area = ½ × base × height. Converting the measurements to meters (since 1 mm = 0.001 m), we have the base as 0.166 m and the height as 0.930 m. Now, the area can be calculated as:
Area = ½ × 0.166 m × 0.930 m
Area = 0.07719 m2
To express this area to the proper number of significant figures, we observe that '166' has three significant figures and '930.0' has four significant figures, and in multiplication, we use the number with the least amount of significant figures. Therefore, we should round off our answer to three significant figures, resulting in 0.0772 m2.